By Heino Prinz
Enzyme kinetics, binding kinetics and pharmacological dose-response curves are at present analyzed through a number of average equipment. a few of these, like Michaelis-Menten enzyme kinetics, use believable approximations, others, like Hill equations for dose-response curves, are superseded. Calculating real looking response schemes calls for numerical mathematical workouts which typically should not lined within the curricula of lifestyles technology. This textbook will provide a step by step advent to numerical recommendations of non-linear and differential equations. it is going to be followed with a suite of courses to calculate any response scheme on any computer. usual examples from analytical biochemistry and pharmacology can be utilized as flexible templates. while a response scheme is utilized for info becoming, the ensuing parameters will not be detailed. Correlation of parameters could be mentioned and simplification options may be offered.
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Additional info for Numerical Methods for the Life Scientist: Binding and Enzyme Kinetics Calculated with GNU Octave and MATLAB
Example text
6, numerical solutions are approximations, whereas analytical solutions always are correct. m are shown in Fig. 2. m mainly in lines 27 and 29. m) 8e-007 7e-007 6e-007 5e-007 4e-007 3e-007 2e-007 1e-007 0 -1e-007 -2e-007 0 20 40 60 80 100 Concentration of [L] (free ligand) Fig. 2 Differences between numerical and analytical solutions. Bound and free ligand concentrations shown in Fig. 1 were calculated for 1 unit (mM) receptor and an equilibrium dissociation constant of 10 units (mM). 3 are plotted versus the free ligand concentration.
M) 51 The plot command is used to plot the concentrations of all complexes. This is done in line 32. The legend in line 38 (not shown here) is changed accordingly. 3 shows the concentrations of LR, RL and LRL as a function of the free ligand concentration. Note that the concentrations of the monoliganded complexes LR and RL only differ by the same factor at all ligand concentrations. This is a general property of all equilibrium-binding curves, where complexes with the same number of ligands only differ by a given factor at all ligand concentrations.
3 Equilibrium binding to two independent sites. 19), the concentrations of complexes LR (x) RL (+) and LRL (*) are plotted versus the free ligand concentration. The calculated affinities are KD1 ¼ KD3 ¼ 5 mM for the first and KD2 ¼ KD4 ¼ 10 mM for the second site Lines 2 and 8 are required when the name of the program is changed. It is advisable to rename a program every time it is modified. 7) into Octave code. Line 33 is the modified plot command. Note that it is possible to do simple operations like 2*VLR within the plot command, and also note that it is possible to define colors in the plot style (defined with quotes).